Which of the following is true regarding the solutions to the logarithmic equation below?
Accepted Solution
A:
Note that the logarithmic function is determined for all [tex]x>0.[/tex]Now solve the equation:[tex]2\log_3x=4,\\ \\\log_3x^2=4,\\ \\3^{\log_3x^2}=3^4,\\ \\x^2=81,\\ \\x_1=9,\ x_2=-9.[/tex]Since [tex]x_2=-9<0,[/tex] this is an extraneous solution. Since [tex]x_1=9>0,[/tex] this is true solution.Answer: correct option is D